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    Isometries

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    Fix in Consider the real linear map

    given by

    (a) With respect to the basis B = {1, i, j, k}, find the associated matrix for .
    (b) Find the associated matrix A (sub alpha bar) for M (sub alpha bar). Compare with (a).
    (c) Compute det(A sub alpha) and det (A sub alpha bar). Interpret.

    See attached file for full problem description.

    © BrainMass Inc. brainmass.com February 24, 2021, 2:06 pm ad1c9bdddf
    https://brainmass.com/math/matrices/isometries-2406

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    Solution Preview

    In order to be able to write them, I will use a and b instead of alpha and beta; I will also use M_a as a notation for M sub a, and conj(a) will mean a bar (the conjugate of a). The problem does not specify, but I assume H means the algebra of quaternions.
    (a)our element a in H can be uniquely written as x+y*i+z*j+t*k, where x,y,z,t are ...

    Solution Summary

    This shows how to find associated matrices for a given linear map.

    $2.19

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